In the real world, after delivery our message would now be lying on our correspondent's doormat waiting for them to notice it. Sooner or later they will walk past, pick up the letter, open it and read it.
In our computer world, you may not be too surprised by now to realise that things are about the same. Most people have mail programs that take a look at their mailbox (probably stored on a computer run by their network provider) every ten minutes or so for new mail. When their mail program sees a new message, it moves it to their local computer where they can then open the message and read it.